Hifi speakers are assumed to be linear, but in the real world, as they reach their limits they go off track. Then there are guitar speakers and some pro audio speakers, which are designed to be non-linear. They deliberately compress as they are driven louder, which provides better performance in a "live" venue, given the way our ears work. Nor are cabinets linear, once you get beyond mini-monitors driven to merely polite volumes. We also can't get away from our listening rooms, and "linear" means something very different to a carpenter.

The Klippel site sreten mentioned earlier is the current state-of-the-art for chasing down false assumptions. But, hey, we had to simplify things to see the basic pattern before complexicating it with all the stuff that really matters. In the '50s, we were so lost....

See this helps a lot. I mentioned the S-parameter thingy, not to clever, but to describe a measurement metric that behaves well at small signal and then craps out fast as non-linearities kick in. So by floating that concept, I was able to get someone with a good understanding of TS to confirm that they behave the same way as something that I personally am quite familiar with. So to that effect, for me, and for my insight, they are relevant to speaker design. Muchos gracias.

Given that the linked thread is so long, i should give away the ending. A number of TLs (3 cabinets, 1 with 3 variations) that do perform very well for this driver combination were developed and an alternate XO offered up. A number of them have been built and the owners are very pleased with the results. Including at least one who had built the original -- he was able to remove the sub he had used to cover off the original's bass deficit.

welcome to the forums! I too am an engineer, and like to use my engineering "skills" applied to speakers, but I find that the value of my theoretical understanding often pales compared to the experience of many people here. Both in "real life" and in speakers, I find that just trying stuff gets me a lot further than years of study. But certainly you need a bit of both theoretical understanding and practical knowledge.

There's a lot of good reference material on speaker design, and surely still more progress to be made on the electro-acoustical front --- just look at some of the recent concepts at Danley Sound Labs: the tapped horn and the synergy horn show that bass reflex boxes are definitely not the final stage of evolution for speakers, and there is much more to be learned.

However if I may offer a suggestion counter to many of the popular approaches, I would suggest starting at the other end of the signal chain --- the brain. All speakers are designed with a recipient in mind, a human brain. So viewing the nature of the brain and the ear may reveal more about what traits you want the focus of the design of your speaker to be.

I personally have the book Psychoacoustics by Fastl & Zwicker, which is more or less a reference book of most of our current understanding of psychoacoustics and human auditory perception. It's pretty theoretical, and not directly applicable to speaker design without a few steps of abstraction, but I think the "Munich school of acoustics" is a promising approach in optimizing a speaker to get the best perceived sound. Sure, one could come up with criteria for an ideal speaker without regarding the ear at all --- unity transfer function, dirac impulse response, point source, etc --- but as this perfect speaker is surely not possible in practice, it helps to know which areas you will want to focus on in a compromise design.

Last but not least: experiment. A lot. Build proven designs (Troels Gravesen, Zaph and planet10 come to mind), run simulations (I like HornResp, other popular choices are the MJK worksheets, AkAbak, WinISD Pro and many more), listen to speakers and see for yourself how changes affect the sound. Full range designs are very easy to play around with, you can easily try different enclosure types and compare the effect without having to deal with the crossover at the same time, but they come with their own set of limitations. Even if you don't intend to have a full range as your perfect speaker, there is much to be learned from them.